Motion correction systems and methods of propeller magnetic resonance images

ABSTRACT

A magnetic resonance (MR) imaging method of correcting motion in precorrection MR images of a subject is provided. The method includes applying, by an MR system, a pulse sequence having a k-space trajectory of a blade being rotated in k-space. The method also includes acquiring k-space data of a three-dimensional (3D) imaging volume of the subject, the k-space data of the 3D imaging volume corresponding to the precorrection MR images and acquired by the pulse sequence. The method further includes receiving a 3D MR calibration data of a 3D calibration volume, wherein the 3D calibration volume is greater than or equal to the 3D imaging volume, jointly estimating rotation and translation in the precorrection MR images based on the k-space data of the 3D imaging volume and the calibration data, correcting motion in the precorrection images based on the estimated rotation and the estimated translation, and outputting the motion-corrected images.

BACKGROUND

The field of the disclosure relates generally to systems and methods ofmotion correction, and more particularly, to systems and methods ofmotion correction of magnetic resonance (MR) images acquired byPROPELLER (Periodically Rotated Overlapping ParallEL Lines with EnhancedReconstruction).

Magnetic resonance imaging (MRI) has proven useful in diagnosis of manydiseases. MRI provides detailed images of soft tissues, abnormal tissuessuch as tumors, and other structures, which cannot be readily imaged byother imaging modalities, such as computed tomography (CT). Further, MRIoperates without exposing patients to ionizing radiation experienced inmodalities such as CT and x-rays.

Although compared to Cartesian sampling PROPELLER sampling scheme isrelatively insensitive to motion, motion correction is needed forPROPELLER sampling to reduce artifacts introduced by motion. Knownmotion correction is disadvantaged in some aspects and improvements aredesired.

BRIEF DESCRIPTION

In one aspect, a magnetic resonance (MR) imaging method of correctingmotion in precorrection MR images of a subject is provided. The methodincludes applying, by an MR system, a pulse sequence having a k-spacetrajectory of a blade being rotated in k-space, the blade including aplurality of views. The method also includes acquiring k-space data of athree-dimensional (3D) imaging volume of the subject, the k-space dataof the 3D imaging volume corresponding to the precorrection MR imagesand acquired by the pulse sequence. The method further includesreceiving a 3D MR calibration data of a 3D calibration volume, whereinthe 3D calibration volume is greater than or equal to the 3D imagingvolume, jointly estimating rotation and translation in the precorrectionMR images based on the k-space data of the 3D imaging volume and thecalibration data, correcting motion in the precorrection images based onthe estimated rotation and the estimated translation, and outputting themotion-corrected images.

In another aspect, a motion correction system of correcting motion inprecorrection MR images of a subject is provided. The system includes amotion correction computing device, the motion correction computingdevice comprising at least one processor in communication with at leastone memory device. The at least one processor is programmed to receivek-space data of a 3D imaging volume of the subject, the k-space data ofthe 3D imaging volume corresponding to the precorrection MR images andacquired by a pulse sequence having a k-space trajectory of a bladebeing rotated in k-space, the blade including a plurality of views. Theat least one processor is also programmed to receive a 3D MR calibrationdata of a 3D calibration volume, wherein the 3D calibration volume isgreater than or equal to the 3D imaging volume. The at least oneprocessor is further programmed to jointly estimate rotation andtranslation in the precorrection MR images based on the k-space data ofthe 3D imaging volume and the calibration data, correct motion in theprecorrection images based on the estimated rotation and the estimatedtranslation, and output the motion-corrected images.

DRAWINGS

FIG. 1 is a schematic diagram of an exemplary magnetic resonance imaging(MRI) system.

FIG. 2A is a schematic diagram of a k-space trajectory of a PROPELLER(Periodically Rotated Overlapping ParallEL Lines with EnhancedReconstruction) sampling scheme.

FIG. 2B is schematic diagram of a blade in the sampling scheme shown inFIG. 2A.

FIG. 3A is a comparison of images acquired by PROPELLER and imagesacquired by Cartesian fast spin echo.

FIG. 3B is a comparison of images acquired by PROPELLER and imagesacquired by echo planar imaging.

FIG. 4A is a flow chart of a known motion correction method of imagesacquired by PROPELLER.

FIG. 4B a comparison of an image without motion correction and an imagewith the known motion correction shown in FIG. 4A.

FIG. 4C shows images of neighboring slices with the known motioncorrection shown in FIG. 4A.

FIG. 4D is comparison of an image of an edge slice without motioncorrection and an image of the edge slice with the known motioncorrection shown in FIG. 4A.

FIG. 5A is schematic diagram of an exemplary motion correction system.

FIG. 5B is a flow chart of an exemplary method of motion correction.

FIG. 6 is a flow chart of an exemplary method of jointly estimatingrotation and translation.

FIG. 7 is a comparison of images motion-corrected by the known methodshown in FIG. 4A and images motioned-corrected by the systems andmethods shown in FIGS. 5A-6.

FIG. 8 is another comparison of images motion-corrected by the knownmethod shown in FIG. 4A and with images motioned-corrected by thesystems and methods shown in FIGS. 5A-6.

FIG. 9 is a block diagram of an exemplary computing device.

DETAILED DESCRIPTION

The disclosure includes systems and methods of motion correction ofmagnetic resonance (MR) images acquired by a PROPELLER (PeriodicallyRotated Overlapping ParallEL Lines with Enhanced Reconstruction)technique of a subject. As used herein, motion correction or correctingmotion of an image is transforming the image back to a state wheremotion does not occur, or reducing or removing artifacts caused bymotion. A subject is a human, an animal, or a phantom. Motion correctionfor slices of images acquired by 2D PROPELLER is described herein as anexample only. The systems and methods disclosed herein may be applied tomotion correction of images acquired by PROPELLER in 3D, such as imagesacquired by PROPELLER in a plurality of slice-encoding steps. Methodaspects will be in part apparent and in part explicitly discussed in thefollowing description.

In magnetic resonance imaging (MRI), a subject is placed in a magnet.When the subject is in the magnetic field generated by the magnet,magnetic moments of nuclei, such as protons, attempt to align with themagnetic field but precess about the magnetic field in a random order atthe nuclei's Larmor frequency. The magnetic field of the magnet isreferred to as B0 and extends in the longitudinal or z direction. Inacquiring an MRI image, a magnetic field (referred to as an excitationfield B1), which is in the x-y plane and near the Larmor frequency, isgenerated by a radio-frequency (RF) coil and may be used to rotate, or“tip,” the net magnetic moment Mz of the nuclei from the z direction tothe transverse or x-y plane. A signal, which is referred to as an MRsignal, is emitted by the nuclei, after the excitation signal B1 isterminated. To use the MR signals to generate an image of a subject,magnetic field gradient pulses (Gx, Gy, and Gz) are used. The gradientpulses are used to scan through the k-space, the space of spatialfrequencies or inverse of distances. A Fourier relationship existsbetween the acquired MR signals and an image of the subject, andtherefore the image of the subject can be derived by reconstructing theMR signals.

FIG. 1 illustrates a schematic diagram of an exemplary MRI system 10. Inthe exemplary embodiment, the MRI system 10 includes a workstation 12having a display 14 and a keyboard 16. The workstation 12 includes aprocessor 18, such as a commercially available programmable machinerunning a commercially available operating system. The workstation 12provides an operator interface that allows scan prescriptions to beentered into the MRI system 10. The workstation 12 is coupled to a pulsesequence server 20, a data acquisition server 22, a data processingserver 24, and a data store server 26. The workstation 12 and eachserver 20, 22, 24, and 26 communicate with each other.

In the exemplary embodiment, the pulse sequence server 20 responds toinstructions downloaded from the workstation 12 to operate a gradientsystem 28 and a radiofrequency (“RF”) system 30. The instructions areused to produce gradient and RF waveforms in MR pulse sequences. An RFcoil 38 and a gradient coil assembly 32 are used to perform theprescribed MR pulse sequence. The RF coil 38 is shown as a whole body RFcoil. The RF coil 38 may also be a local coil that may be placed inproximity to the anatomy to be imaged, or a coil array that includes aplurality of coils.

In the exemplary embodiment, gradient waveforms used to perform theprescribed scan are produced and applied to the gradient system 28,which excites gradient coils in the gradient coil assembly 32 to producethe magnetic field gradients G_(x), G_(y), and G_(z) used for frequencyencoding, phase encoding, and slice selection/encoding of MR signals.The gradient coil assembly 32 forms part of a magnet assembly 34 thatalso includes a polarizing magnet 36 and the RF coil 38.

In the exemplary embodiment, the RF system 30 includes an RF transmitterfor producing RF pulses used in MR pulse sequences. The RF transmitteris responsive to the scan prescription and direction from the pulsesequence server 20 to produce RF pulses of a desired frequency, phase,and pulse amplitude waveform. The generated RF pulses may be applied tothe RF coil 38 by the RF system 30. Responsive MR signals detected bythe RF coil 38 are received by the RF system 30, amplified, demodulated,filtered, and digitized under direction of commands produced by thepulse sequence server 20. The RF coil 38 is described as a transmitterand receiver coil such that the RF coil 38 transmits RF pulses anddetects MR signals. In one embodiment, the MRI system 10 may include atransmitter RF coil that transmits RF pulses and a separate receivercoil that detects MR signals. A transmission channel of the RF system 30may be connected to a RF transmission coil and a receiver channel may beconnected to a separate RF receiver coil. Often, the transmissionchannel is connected to the whole body RF coil 38 and each receiversection is connected to a separate local RF coil.

In the exemplary embodiment, the RF system 30 also includes one or moreRF receiver channels. Each RF receiver channel includes an RF amplifierthat amplifies the MR signal received by the RF coil 38 to which thechannel is connected, and a detector that detects and digitizes the Iand Q quadrature components of the received MR signal. The magnitude ofthe received MR signal may then be determined as the square root of thesum of the squares of the I and Q components as in Eq. (1) below:M=√{square root over (I ² +Q ²)}  (1);and the phase of the received MR signal may also be determined as in Eq.(2) below:

$\begin{matrix}{\varphi = {{\tan^{- 1}\left( \frac{Q}{I} \right)}.}} & (2)\end{matrix}$

In the exemplary embodiment, the digitized MR signal samples produced bythe RF system 30 are received by the data acquisition server 22. Thedata acquisition server 22 may operate in response to instructionsdownloaded from the workstation 12 to receive real-time MR data andprovide buffer storage such that no data is lost by data overrun. Insome scans, the data acquisition server 22 does little more than passthe acquired MR data to the data processing server 24. In scans thatneed information derived from acquired MR data to control furtherperformance of the scan, however, the data acquisition server 22 isprogrammed to produce the needed information and convey it to the pulsesequence server 20. For example, during prescans, MR data is acquiredand used to calibrate the pulse sequence performed by the pulse sequenceserver 20. Also, navigator signals may be acquired during a scan andused to adjust the operating parameters of the RF system 30 or thegradient system 28, or to control the view order in which k-space issampled.

In the exemplary embodiment, the data processing server 24 receives MRdata from the data acquisition server 22 and processes it in accordancewith instructions downloaded from the workstation 12. Such processingmay include, for example, Fourier transformation of raw k-space MR datato produce two or three-dimensional images, the application of filtersto a reconstructed image, the generation of functional MR images, andthe calculation of motion or flow images.

In the exemplary embodiment, images reconstructed by the data processingserver 24 are conveyed back to, and stored at, the workstation 12. Insome embodiments, real-time images are stored in a database memory cache(not shown in FIG. 1, from which they may be output to operator display14 or a display 46 that is located near the magnet assembly 34 for useby attending physicians. Batch mode images or selected real time imagesmay be stored in a host database on disc storage 48 or on a cloud. Whensuch images have been reconstructed and transferred to storage, the dataprocessing server 24 notifies the data store server 26. The workstation12 may be used by an operator to archive the images, produce films, orsend the images via a network to other facilities.

The systems and methods disclosed herein are used to reduce or removemotion artifacts in images acquired by PROPELLER. Compared to otherimaging modalities, MRI is unique in that an MRI signal is representedby a complex number, rather than a scalar or a real number. The imagevalue for each image pixel, therefore, includes a magnitude and a phase.Complex MR images may be reconstructed based on I and Q quadrature MRsignals, using processes such as Fourier transform.

FIGS. 2A-2B show a PROPELLER k-space sampling scheme. FIG. 2A is aschematic diagram of a k-space trajectory 200 of a PROPELLER samplingscheme. FIG. 2B shows a blade 202 in the PROPELLER sampling scheme. APROPELLER sampling scheme is a scheme of sampling the k-space by aPROPELLER pulse sequence, where the k-space is sampled by rotatingblades 202 with each blade 202 having a plurality of views 206. An imageacquired by PROPELLER may be referred to as a PROPELLER image. In MR, apulse sequence is a sequence of RF pulses, gradient pulses, and dataacquisition applied by the MRI system 10 in acquiring MR signals. Asdescribed above, in MRI, the MR signals are acquired by sampling thek-space with gradients Gx, Gy, Gz, which correspond tokx/frequency-encoding direction, ky/phase-encoding direction, andkz/slice-encoding direction. An MR image can be reconstructed from theMR signals using Fourier transform. The k-space is typically sampledalong a Cartesian grid, where the k-space sampling points are in arectilinear pattern. The advantage of Cartesian sampling is that datapoints are regularly spaced and can be placed directly into standardarray processors designed for fast Fourier Transform (FFT) computations.The disadvantage of Cartesian sampling is the Cartesian samplingmethod's sensitivity to motion.

A PROPELLER pulse sequence does not sample the k-space along theCartesian grid. Instead, a PROPELLER pulse sequence samples the k-spacein a radial pattern, where the k-space lines radially span from thecenter region of the k-space, and is categorized as a radial samplingscheme. Compared to a standard radial acquisition, which samples oneline after an RF excitation pulse, in a PROPELLER sampling scheme, ablade 202 that includes a plurality of views or k-space lines 206 issampled after an RF excitation pulses through fast spin echo sampling orother manners such as gradient echo. The number of views 206 in oneblade 202 typically may be between 16 and 32. The views 206 in a blade202 are generally parallel to one another, where a center view 206-c ofthe blade 202 may go through the center 208 of the k-space. After ablade 202 at a certain angle is acquired, the blade 202 rotates by anangle at which time second, third, and so on sets of data are acquired.This process continues until MR data from the entire k-space circle havebeen collected.

The major benefit of radial sampling is its relative insensitivity tomotion. Unlike Cartesian sampling, radial sampling does not have fixedfrequency and phase-encoding directions. Noise from moving anatomicstructures does not propagate as discrete ghosts, blurring, or artifactsalong a single phase-encoding direction. In radial sampling, such noiseis distributed diffusely across the entire image. Further, because thecenter region of the k-space is oversampled, all radial lines make equalcontributions to the image and include signals with a relatively-highintensity from the center region of the k-space, unlike Cartesiansampling, which only samples the center region of k-space over a fewlines. As a result, motion during one or a few radial lines has lesslikelihood to severely degrade image quality. Moreover, in PROPELLER,the center region R is sampled by all blades 202. This redundancy may beused to estimate motion and therefore to correct motion.

FIGS. 3A and 3B show a contrast of images 302, 304, 305 acquired byPROPELLER with images 306, 308, 309 acquired by Cartesian sampling overthe same region of anatomy and with the same matrix size and field ofview (FOV). The image 306 was acquired by Cartesian fast spin echo(FSE). The image 308, 309 was acquired by echo planar imaging (EPI). Theimages 305, 309 are diffusion-weighted images. The PROPELLER image 302is less blurry and more homogeneous than the FSE image 306. Similarly,the PROPELLER image 304, 305 has less image distortion and is moreuniform than the EPI image 308, 309.

FIGS. 4A-4D show a known motion correction method 400 and images withoutand with motion correction by the method 400. The assumption of theknown method 400 is that motion parameters may be estimated from thek-space data. The method 400 includes estimating and correcting 402rotation of the MR data using magnitude k-space data. The magnitudek-space data M_(n) at the center region R from each blade 202 (FIG. 2)are gridded onto R and averaged together to form a reference k-spacedata M_(A). Each M_(n) is rotated by a series of angles and gridded ontoR for each angle. For each blade 202, the correlation of M_(n) withM_(A) is calculated as a function of the rotation angle. The maximum ofthe calculated correlations is when M_(n) is rotated to M_(A), Thecorrelation, as a function of the rotation angle, is fitted to asecond-order polynomial function, and the peak of the polynomialfunction is the estimated angle of rotation for the blade 202. Once therotation angles for all blades 202 are estimated, coordinates of eachblade are rotated by the estimated rotation angle for that blade. Thatis, the rotation portion of motion correction is completed.

The translation is then estimated and corrected 404 using the complexk-space data D_(n) at the center region R with the rotation-correctedcoordinates. Similar to rotation estimation, complex rotation-correctedk-space data D_(n) at the center region R for all blades 202 areaveraged to derive an averaged complex data D_(A). In estimatingtranslation, complex conjugate D_(A)* of D_(A) is multiplied by D_(n),and Fourier transform is applied to the product. Then the peak magnitudeof the Fourier transformed product is identified, and a three-pointparabolic fit of the magnitude about the peak in the x and y directionis performed. The location of the vertex of this parabola is theestimated translation in the x and y directions, and a correspondinglinear phase is removed from the collected data for that blade 202 tocorrect translation portion of the motion, because translation in thereal or image space x-y corresponds to a linear phase change in thek-space kx-ky. At this point, the k-space data are motion corrected orrotation and translation corrected. This motion correction is performedslice by slice. That is, the motion correction only corrects in-planemotion, motion that occurred within the slice.

After the motion correction 400 is performed, correlation thresholdingmay be performed to discard or apply low weights to k-space data fromblades 202 corresponding to significant through-plane motion,uncorrected nonrigid body motion, or other factors that would createartifacts in the final reconstructed images. The final image isreconstructed using the correlation weighted k-space data from blades202 by gridding the correlation weighted k-space data and applying aFourier transform.

The method 400 assumes that motion is mostly in-plane rigid motion andthat motion can be estimated based on the phase and signal changes ofthe k-space data. This assumption, however, is not always correct. Themethod 400 therefore has several drawbacks. Firstly, through-planemotion is not corrected. FIG. 4B shows a coronal image 412 acquired byPROPELLER without using the motion correction method 400 and a coronalimage 414 based on the same k-space data but with the motion correction400. Although the motion corrected image 414 has reduced motionartifacts 416 compared to uncorrected image 412, motion artifacts 416are still present in the image 414 because the method 400 only correctsin-plane motion artifacts. Secondly, each slice is aligned separatelyand therefore the slices may be misaligned. FIG. 4C shows axial images418, 420 of two neighboring slices (i.e., slices next to one another) inthe brain and a sagittal image 422 generated based on a series of axialimages including the images 418, 420. For images shown in FIG. 4C, aseries of axial slices are acquired by a PROPELLER pulse sequence, theaxial images are motion corrected by the method 400, and using the axialimages, sagittal images are generated show the images from a differentorientation. In MR, to minimize cross-talks between slice profiles ofneighboring slices of slice-selective RF pulses, even slices and oddslices may be acquired in different passes. The subject may have movedbetween acquisition of different passes. In the motion correction 400,individual axial images 418, 420 are aligned independently from oneanother. As a result, the slices are misaligned, which is presented as azig-zagged pattern 424 along the slice direction 423 in the sagittalimage 422.

Thirdly, because rotation is estimated and corrected 402 beforeestimation and correction 404 of translation in the method 400, themethod 400 heavily depends on the robustness in rotation estimation andcorrection. For edge axial slices of the brain, when the anatomypresents itself as relatively round and symmetrical, rotation estimationfails (FIG. 4D). FIG. 4D shows an axial image 426 based on k-space dataacquired by PROPELLER without motion correction 400 and an axial image428 based on the same acquired k-space data but with the motioncorrection 400. The motion-corrected image 428 has much lower imagequality than the uncorrected image 426. For example, themotion-corrected image 428 has a greatly-increased number of artifacts416. More importantly, the rotation estimation is so inaccurate that theestimated rotation is not usable. That is, rotation estimation andcorrection 402 in the method 400 failed for the edge slice.

Fourthly, the method 400 is only effective for brain images and tends tofail when applied to PROPELLER images of other anatomies in the bodybecause the method 400 does not correct through-plane motion and otheranatomies in the body has more through-planes motion from respiratorymotion and/or cardiac motion. Finally, the motion correction 400 tendsto fail for an imaging volume that is off iso-center (or off-centerimaging volume or region) of the magnet 36 (see FIG. 1). The magneticfield of the system 10 at locations away from the iso-center of themagnet 36 is not as uniform as locations near or at the iso-center, andthis nonuniformity presents as phase variations in the k-space data.Because motion estimation and correction in the method 400 is based oncomplex k-space data that includes the phase information, the method 400tends to fail for off-center anatomies, such as wrists, knees, orshoulder in musculoskeletal (MSK) imaging.

Systems and methods described herein are used to address the problemsassociated with the method 400. Instead of based on the k-space data,the motion correction systems and methods described herein are based onimages to derive motion parameters. The systems and methods describedherein correct both in-plane and through-plane motion in the imagespace, instead of only correcting in-plane motion in the k-space andthrowing away k-space data containing through-plane motion and otherundesired factors. Through-plane motion may be corrected through sliceto volume registration. The systems and methods described herein arerobust and broaden the application of motion correction of PROPELLERimages to the edge slices of the brain, to other anatomies in the bodybesides the brain, to off-center imaging volumes, and todiffusion-weighted imaging.

FIG. 5A is a schematic diagram of an exemplary motion correction system500. In the exemplary embodiment, the system 500 includes a motioncorrection computing device 502 configured to correct motion of MRimages. The motion correction computing device 502 may be included inthe workstation 12 of the MRI system 10, or may be included in aseparate computing device that is in communication with the workstation12, through wired or wireless communication. In some embodiments, themotion correction computing device 502 is a separate computing devicefrom the workstation 12 and receives MR images acquired by theworkstation 12 through a portable storage device, such as a flash driveor a thumb drive.

FIG. 5B is a flow chart of an exemplary method 550 of correcting motionin images acquired by a PROPELLER pulse sequence. The method 550 may beimplemented on the motion correction computing device 502. The method550 includes receiving 552 k-space data of a three-dimensional (3D)imaging volume of the subject, the k-space data of the 3D imaging volumecorrespond to precorrection MR images and were acquired by an MR systemby rotating a blade in the k-space, each blade including a plurality ofviews. The k-space data may be acquired by a PROPELLER sequence inslices or in a two-dimensional (2D) manner, where the 3D imaging volumeincludes a plurality of slices, a slice is selected by a z gradient, andthe kx-ky plane corresponding to that slice is sampled in a PROPELLERmanner, i.e., by rotating a blade in the kx-ky plane of that slice.Alternatively, the k-space data may be acquired by a PROPELLER sequencein a plurality of slice-encoding steps or in a 3D manner. For example,the 3D k space (kx-ky-kz) is sampled by stacks of blade sampling ofkx-ky planes along the kz direction. kz corresponds to a slice encodingstep. That is, the k-space data are acquired by rotating a blade in akx-ky plane corresponding to a slice-encoding step. Final images arederived by applying a Fourier transform in the kz dimension, as well asin the kx and ky dimensions. The 3D k-space data may be Fouriertransformed in the kz direction to derive k-space data of a plurality ofslices, which are processed similarly to k-spaced data acquired in a 2Dmanner.

In the exemplary embodiment, the method 550 also includes receiving 554a 3D MR calibration data of a 3D calibration volume. The calibrationdata is obtained in a separate acquisition. For example, a calibrationscan is typically used in MR scans for calculating coil sensitivity mapsof multi-coils and other scan parameters. Therefore, the systems andmethods described herein do not require extra scanning or increase thetotal scan time. The calibration data may be k-space data, images, or acombination thereof. The 3D imaging volume is equal to or smaller thanthe 3D calibration volume. Further, the method 550 includes jointlyestimating rotation and translation based on the k-space data of the 3Dimaging volume and the calibration data. Unlike the method 400, whererotation is estimated and corrected before translation is estimated andcorrected, in the exemplary embodiment, rotation and translation arejointly estimated in the same operation, and are jointly corrected inthe same operation. The method 550 also includes 558 correcting motionin the precorrection images based on the estimated rotation and theestimated translation. Moreover, the method 550 includes outputting 560the motion-corrected image.

FIG. 6 is a flow chart of an exemplary embodiment of jointly estimating556 rotation and translation. k-space data acquired in slices are usedas an example for illustration only. The systems and methods may beapplied to k-space data acquired in a plurality of slice-encoding steps.In the exemplary embodiment, for each slice in the plurality of slices,rotation and translation are jointly 602 estimated for each blade in theslice. The estimation is performed in the image space. In someembodiments, rotation and translation are estimated by imageregistration. For example, to estimate motion in an image I, a functionof the differences between a transformed image of the image I and atarget image/a template image is optimized, with motion parameters suchas rotation and translation as the optimizing variables. The transformedimage is the image I being transformed with motion parameters, such asrotation and translation. In PROPELLER, the k-space data in the centerregion R are sampled by all blades 202 (see FIG. 2). The center region Ris within a circle having L/FOV in diameter, where L is the number views206 in one blade 202. For each blade, the k-space data in the centerregion R may be referred to as center k-space data of the blade and bedenoted as S_(n). A center image of a blade may be reconstructed basedon the center k-space data of the blade S_(n). A center image as usedherein refers to an image reconstructed from the center k-space data,either for a blade 202 when using the center k-space data S_(n) of theblade 202 or for the slice when using the center k-space data of allblades 202 in that slice. In one example, the center k-space data of theblade is gridded onto a Cartesian grid and then a Fourier transform isperformed on the gridded center k-space data of the blade to derive thecenter image of the blade. In estimating blade rotation and bladetranslation, a template image is a center image of the slice, which isreconstructed based on the center k-space data of the slice. In oneexample, the center k-space data of the slice is derived by gridding thecenter k-space data of each blade S_(n) to a Cartesian grid, combiningthe gridded centered k-spaced data of the blades in the slice, andaveraging the combined k-space data over the number of blades 202. Thecenter k-space image of the slice is reconstructed using methods such asperforming a Fourier transform on the center k-space data of the slice.As a result, blade rotation and blade translation of each blade areestimated based on the center image of the blade and the center image ofthe slice.

In the exemplary embodiment, the translation for each blade is thenfine-tuned 604 because in jointly estimating 602 rotation andtranslation, the translation is estimated based on low resolution imagesreconstructed from the center k-space data S_(n) of the blade and thecenter k-space data of the slice, and was limited by interpolationmethods. In fine-tuning 604, the translation is also estimated byoptimizing a difference function between a transformed image and atemplate image. Different from jointly estimating 602, in fine-tuning604, the optimization is repeated and during each repetition, thetemplate image is updated with estimated translation from the previousiteration, i.e., the template image is translation corrected with thetranslation estimated in the previous iteration. As such, the estimatedtranslation has an increased accuracy than that estimated withoutfine-tuning 604.

In the exemplary embodiment, once the rotation and translation areestimated for all blades 202, the k-space data is motion corrected. Forexample, for each blade, the coordinates of the k-space data of thatblade are rotated with the estimated blade rotation and a linear phaseproportional to the estimated blade translation is removed from thek-space data of that blade. In some embodiments, fine-tuning 604 may beskipped, where motion correction uses rotation and translation estimatedin jointly estimating 602. The motion corrected k-space data at thecenter region R for blades in a slice are combined 606 to reconstruct alow-resolution center image of the slice. In some embodiments, thek-space data is not motion corrected and the center k-space data S_(n)are combined 606 to derive a low-resolution center image of the slice.Jointly estimating 602 and fine-tuning 604 is repeated first for allblades in a slice and then for all slices in the 3D imaging volume.Combining 606 is repeated for all slices in the 3D imaging volume. As aresult, a plurality of center images of the 3D image volume are derived.

In the depicted embodiment, the calibration data may be volumereformatted 608. If the calibration data are k-space data or a mixtureof k-space data with images, the calibration data or k-space data of thecalibration data are reconstructed into images of a plurality of slicesin the 3D calibration volume, The 3D calibration volume may be greaterthan the 3D imaging volume, or the calibration scan may have differentslice numbers and orientations. The calibration data is resliced andreoriented such that the slices in the 3D calibration volume match theslices in the 3D imaging volume. That is, each slice in the 3Dcalibration volume and its corresponding slice in the 3D imaging volumeare of the same anatomical location. Reformatting 608 may be skipped ifthe 3D calibration volume and 3D imaging volume are the same and theslices in the calibration and imaging volumes already match. Contrastnormalization 610 may be performed on the reformatted 3D calibrationdata. Because the calibration data are acquired with different pulsesequences, matrix sizes, resolutions, and scan parameters from thek-space data of the 3D imaging volume, the contrast of the calibrationdata may be different from the images acquired by a PROPELLER sequence.Contrast normalization 610 is used to transform the calibration imagesto have the same or similar contrast as the images in the 3D imagingvolume. In some embodiments, the contrast of images of the 3D imagingvolume acquired by the PROPELLER sequence is also normalized andcontrast of the normalized calibration images and contrast of thenormalized images in the 3D imaging volume are the same or similar.

In the exemplary embodiment, slice rotation and slice translation arejointly estimated 612 based on the reformatted and/or normalizedcalibration images and the center images of the slices derived aftercombining 606 the center k-space data of the blades. In someembodiments, the contrast in images of the 3D imaging volume is alsonormalized, and jointly estimating 612 is based on the reformattedand/or normalized calibration images and normalized center images of theslices. Calibration data are acquired much faster than PROPELLER k-spacedata. For example, for the same 3D volume, calibration data takeapproximately 2-6 seconds, while PROPELLER k-space data take minutes. Asa result, calibration data contain much less motion than PROPELLERk-space data and can serve as a much better reference in motionestimation than center images, thereby increasing the accuracy of motionestimation. Further, because slices in PROPELLER k-space data areregistered to a common reference of calibration data, motion estimationis consistent from slice to slice, compared to the method 400. Slicerotation and slice translation of a slice may be estimated byregistering the center image of the slice to the calibration image ofthe corresponding slice through optimization of a function of thedifferences between a transformed image of the center image of the sliceand the calibration image of the slice, using the calibration image ofthe slice as the template image. Slice rotation and slice translationare estimated 612 slice by slice. That is, jointly estimating 612 slicerotation and slice translation is repeated for the plurality of slicesin the 3D imaging volume. In some embodiments, translation is fine-tuned614. Similar to fine-tuning 604 blade translation, fine-tuning 614 slicetranslation is performed iteratively. The optimization process inestimating slice translation is repeated with the template image isupdated with translation corrected template image based on translationestimated in the previous iteration. Because the resolution of thecenter image is based only the center k-space data, the resolution ofthe center image is low. Fine-tuning 614 slice translation improves theestimation accuracy of slice translation. In some embodiments,fine-tuning 614 slice translation is skipped. In some embodiments,through-plane motion may be estimated by registering slices in the 3Dimaging volume to the 3D calibration volume. The estimated through-planemotion may be combined with blade rotation and translation and slicerotation and translation to correct motion in the PROPELLER images.

In the exemplary embodiment, blade rotation and translation and slicerotation and translation are combined 616 to derive the final bladerotation and final blade translation for each blade in the 3D imagingvolume. For example, final rotation is the sum of blade rotation andslice rotation, and final translation is computed as: finaltranslation=blade translation*exp(i*(slice rotation))+slice translation.

In the exemplary embodiment, once the final blade rotation and finalblade translation are estimated, motion is corrected 558 using theestimated final blade rotation and final blade translation. For example,the k-space data for each blade 202 is rotation-corrected with theestimated final blade rotation, where the k-space coordinates (kx, ky)are multiplied by a rotation matrix

${{R(\theta)} = \begin{bmatrix}{\cos\theta} & {{- {s{in}}}\theta} \\{\sin\theta} & {\cos\theta}\end{bmatrix}},$where θ is the rotation. The k-space data for each blade 202 is alsotranslation-correction with the estimated final blade translation, wherea linear phase proportional to the translation is removed from thek-space data of the blade. Different from the motion correction incombining 606 center k-space data, in motion correction 558, thecorrection is performed on the entire blade or the entire k-space dataof the blade. Because the final blade rotation and translationcorrespond to each blade in each slice, each slice is motion-correctedindependently, thereby allowing fast reconstruction using parallelprocessing, where images or k-space data of slices or slice-encodingdirections are split into two or more passes, which are processedseparately and in parallel with one another.

FIG. 7 is a comparison of images 702, 704 motion-corrected by the knownmethod 400 and image 706, 708 motion-corrected by the methods andsystems described herein. The images 702, 706 are coronal images basedon slices of axial images. The images 704, 708 are sagittal images basedon slices of axial images. The images 702-708 are based on the samek-space data. Compared to the images 702, 704 motion-corrected with theknown method 400, the zig-zagged patterns 424 are greatly reduced in theimages 706, 708 motion-corrected with the methods and systems describedherein. That is, the slices are aligned with one another in the method550.

FIG. 8 is a further comparison of images 801, 803 motion-corrected bythe known method 400 and image 805, 807 motion-corrected by the method550. The images 801, 805 are axial images of a slice close to the top ofthe head, and are acquired with a PROPELLER pulse sequence and withviews 206 in each blade 202 acquired sequentially. The image 801 hasmuch more discernible crosshatching and ripple artifacts than the image805 and is not as sharp as the image 805. The images 803, 807 are imagesof a motion phantom, and are acquired using a PROPELLER pulse sequenceand with views 206 in each blade 202 acquired in a center-out manner.The image quality of the image 803 is deteriorated to the point that theimage 803 is unusable, indicating the known method 400 failed in motioncorrection.

Referring back to FIG. 2, each blade 202 includes a plurality of views206. In acquiring the blade 202, the views 206 may be acquiredsequentially, where the views are acquired in order, either startingfrom the bottom view 206-b and going up or starting from the top view206-t and going down. The views 206 may be acquired in a center-outmanner, where the views are acquired starting from a center view 206-c,which is a view crossing the center 208 of the k-space or view(s) havinga relatively shorter distance to the center 208 than other views 206,and moving outwards. As used herein, a distance from a point (e.g., thecenter 208) to a line (e.g., a view 206) is the perpendicular distanceof the point to the line. Views 206 that are farther out from the center208 may be referred to as peripheral views 206-p. For example, if ablade 202 includes eight views as 206-1 to 206-8 with 206-4 as thecenter view 206-c. In a center-out manner, 206-4 is acquired first, then206-5 or 206-3, 206-6 or 206-2, 206-7 or 206-1, and then 206-8. Becausethe center view 206-c is closer to the center 208 of the k-space, thesignal intensity of the center view 206-c is higher than that ofperipheral views 206-p. Because signal-to-noise ratio (SNR) in diffusionweighted imaging (DWI) is low especially for high b-values, to maximizethe signal acquired by DWI using DW PROPELLER, for each blade 202, viewsare acquired in a center-out manner, taking advantage that center views206-c have higher signal intensity then peripheral views 206-p. However,peripheral views 206-p are at k-space locations with at higher spatialfrequencies and have more detailed information of spatial locations thanthe center views 206-c. Signals from peripheral views 206-p aretherefore needed for motion correction. As a result, the increased SNRsacrifices signals from k-space locations with higher spatialfrequencies. Because the known method 400 uses k-space data to estimatemotion, the method 400 heavily depends on signal modulation of thek-space data, and fails in estimating motion due to the reduced signalsfrom higher spatial frequencies in a center-out acquisition. Incontrast, the systems and methods described herein are image-basedmotion estimation, break the assumption that signal fluctuation in thek-space data comes only from in-plane motion, and instead use imagestructures to estimate the motion parameters based on the calibrationdata as a common reference. As a result, the systems and methods hereinare robust in motion correction.

Referring back to FIG. 8, image quality of the image 803, which ismotion-corrected by the known method 400, is much worse than that of theimage 807, which is motioned corrected by the method 550. Image qualityof the image 803 is even worse than an image without motion correction(not shown). Therefore, the known motion-correction method 400 typicallyis not performed in DWI PROPELLER. In contrast, the method 550 works forsequential or center-out views (see images 803, 807). The method 550,therefore, may be used for motion correction of DWI PROPELLER images. Incorrecting motion in DW images, the motion correction is performed foreach diffusion-weighting direction and on images without diffusionweighting (T2 images) separately. For example, if DW images in x-, y-,and z-diffusion directions and a T2 image for each slice are acquired,the method 550 is performed for x-, y-, and z-diffusion directions andthe T2 images separately before the images from different diffusiondirections are combined and before the DW images and the T2 images areused to further process and analysis such as computation of apparentdiffusion coefficient (ADC) map. This is, the method 550 is repeated foreach diffusion direction and for the T2 images. If a plurality ofb-values are used in diffusion weighting, the method 550 may be repeatedfor each b-value.

The workstation 12 and the motion correction computing device 502described herein may be any suitable computing device 800 and softwareimplemented therein. FIG. 9 is a block diagram of an exemplary computingdevice 800. In the exemplary embodiment, the computing device 800includes a user interface 804 that receives at least one input from auser. The user interface 804 may include a keyboard 806 that enables theuser to input pertinent information. The user interface 804 may alsoinclude, for example, a pointing device, a mouse, a stylus, a touchsensitive panel (e.g., a touch pad and a touch screen), a gyroscope, anaccelerometer, a position detector, and/or an audio input interface(e.g., including a microphone).

Moreover, in the exemplary embodiment, computing device 800 includes adisplay interface 817 that presents information, such as input eventsand/or validation results, to the user. The display interface 817 mayalso include a display adapter 808 that is coupled to at least onedisplay device 810. More specifically, in the exemplary embodiment, thedisplay device 810 may be a visual display device, such as a cathode raytube (CRT), a liquid crystal display (LCD), a light-emitting diode (LED)display, and/or an “electronic ink” display. Alternatively, the displayinterface 817 may include an audio output device (e.g., an audio adapterand/or a speaker) and/or a printer.

The computing device 800 also includes a processor 814 and a memorydevice 818. The processor 814 is coupled to the user interface 804, thedisplay interface 817, and the memory device 818 via a system bus 820.In the exemplary embodiment, the processor 814 communicates with theuser, such as by prompting the user via the display interface 817 and/orby receiving user inputs via the user interface 804. The term“processor” refers generally to any programmable system includingsystems and microcontrollers, reduced instruction set computers (RISC),complex instruction set computers (CISC), application specificintegrated circuits (ASIC), programmable logic circuits (PLC), and anyother circuit or processor capable of executing the functions describedherein. The above examples are exemplary only, and thus are not intendedto limit in any way the definition and/or meaning of the term“processor.”

In the exemplary embodiment, the memory device 818 includes one or moredevices that enable information, such as executable instructions and/orother data, to be stored and retrieved. Moreover, the memory device 818includes one or more computer readable media, such as, withoutlimitation, dynamic random access memory (DRAM), static random accessmemory (SRAM), a solid state disk, and/or a hard disk. In the exemplaryembodiment, the memory device 818 stores, without limitation,application source code, application object code, configuration data,additional input events, application states, assertion statements,validation results, and/or any other type of data. The computing device800, in the exemplary embodiment, may also include a communicationinterface 830 that is coupled to the processor 814 via the system bus820. Moreover, the communication interface 830 is communicativelycoupled to data acquisition devices.

In the exemplary embodiment, the processor 814 may be programmed byencoding an operation using one or more executable instructions andproviding the executable instructions in the memory device 818. In theexemplary embodiment, the processor 814 is programmed to select aplurality of measurements that are received from data acquisitiondevices.

In operation, a computer executes computer-executable instructionsembodied in one or more computer-executable components stored on one ormore computer-readable media to implement aspects of the inventiondescribed and/or illustrated herein. The order of execution orperformance of the operations in embodiments of the inventionillustrated and described herein is not essential, unless otherwisespecified. That is, the operations may be performed in any order, unlessotherwise specified, and embodiments of the invention may includeadditional or fewer operations than those disclosed herein. For example,it is contemplated that executing or performing a particular operationbefore, contemporaneously with, or after another operation is within thescope of aspects of the invention.

At least one technical effect of the systems and methods describedherein includes (a) motion correction for PROPELLER images of increasedaccuracy; (b) robust motion correction for all slices or slice-encodingsteps and for anatomies besides the brain; (c) image-based motioncorrection; (d) jointly estimating rotation and translation; (e)fine-tuning estimation of translation; (0 motion correction suitable fordiffusion weighted PROPELLER; (g) consistent alignment across slicesafter motion correction without penalty of increase in scan time byaligning to calibration data; and (h) independent motion-correction foreach slice, thereby allowing fast reconstruction using parallelprocessing.

Exemplary embodiments of systems and methods of motion correction aredescribed above in detail. The systems and methods are not limited tothe specific embodiments described herein but, rather, components of thesystems and/or operations of the methods may be utilized independentlyand separately from other components and/or operations described herein.Further, the described components and/or operations may also be definedin, or used in combination with, other systems, methods, and/or devices,and are not limited to practice with only the systems described herein.

Although specific features of various embodiments of the invention maybe shown in some drawings and not in others, this is for convenienceonly. In accordance with the principles of the invention, any feature ofa drawing may be referenced and/or claimed in combination with anyfeature of any other drawing.

This written description uses examples to disclose the invention,including the best mode, and also to enable any person skilled in theart to practice the invention, including making and using any devices orsystems and performing any incorporated methods. The patentable scope ofthe invention is defined by the claims, and may include other examplesthat occur to those skilled in the art. Such other examples are intendedto be within the scope of the claims if they have structural elementsthat do not differ from the literal language of the claims, or if theyinclude equivalent structural elements with insubstantial differencesfrom the literal language of the claims.

What is claimed is:
 1. A magnetic resonance (MR) imaging method ofcorrecting motion in precorrection MR images of a subject, comprising:applying, by an MR system, a pulse sequence having a k-space trajectoryof a blade being rotated in k-space, the blade including a plurality ofviews; acquiring k-space data of a three-dimensional (3D) imaging volumeof the subject, the k-space data of the 3D imaging volume correspondingto the precorrection MR images and acquired by the pulse sequence;receiving a 3D MR calibration data of a 3D calibration volume, whereinthe 3D calibration volume is greater than or equal to the 3D imagingvolume; jointly estimating rotation and translation in the precorrectionMR images based on the k-space data of the 3D imaging volume and thecalibration data; correcting motion in the precorrection images based onthe estimated rotation and the estimated translation; and outputting themotion-corrected images.
 2. A motion correction system of correctingmotion in precorrection magnetic resonance (MR) images of a subject,comprising a motion correction computing device, the motion correctioncomputing device comprising at least one processor in communication withat least one memory device, and the at least one processor programmedto: receive k-space data of a three-dimensional (3D) imaging volume ofthe subject, the k-space data of the 3D imaging volume corresponding tothe precorrection MR images and acquired by a pulse sequence having ak-space trajectory of a blade being rotated in k-space, the bladeincluding a plurality of views; receive a 3D MR calibration data of a 3Dcalibration volume, wherein the 3D calibration volume is greater than orequal to the 3D imaging volume; jointly estimate rotation andtranslation in the precorrection MR images based on the k-space data ofthe 3D imaging volume and the calibration data; correct motion in theprecorrection images based on the estimated rotation and the estimatedtranslation; and output the motion-corrected images.
 3. The method ofclaim 1, wherein jointly estimating rotation and translation furthercomprises: reformatting slices in the 3D calibration volume to matchslices in the 3D imaging volume; and jointly estimating the rotation andthe translation based on the k-space data of the 3D imaging volume andthe reformatted calibration data.
 4. The method of claim 1, whereinjointly estimating rotation and translation further comprises:normalizing contrast in images of the calibration data; and jointlyestimating the rotation and the translation based on the k-space data ofthe 3D imaging volume and the normalized calibration data.
 5. The methodof claim 1, wherein jointly estimating rotation and translation furthercomprises: jointly estimating blade rotation and blade translation ineach blade based on the k-space data of the 3D imaging volume.
 6. Themethod of claim 5, wherein jointly estimating rotation and translationfurther comprises: iteratively fine-tuning the blade translation.
 7. Themethod of claim 1, wherein: acquiring k-space data further comprisesacquiring k-space data of a plurality of slices in the 3D imagingvolume, and wherein for each slice in the plurality of the slices, thek-space data of the 3D imaging volume were acquired by rotating a bladein a kx-ky plane corresponding to the slice; and jointly estimatingrotation and translation further comprises: for each slice in the 3Dimaging volume, combining k-space data in a center region of the bladesof the slice into center k-space data of the slice; and reconstructing acenter image of the slice based on the center k-space data of the slice;and jointly estimating slice rotation and slice translation based oncenter images of the plurality of slices and the calibration data. 8.The method of claim 7, wherein jointly estimating rotation andtranslation further comprises: for each slice in the 3D imaging volume,for each blade in the slice, reconstructing a center image of the bladeusing center k-space data of the blade; jointly estimating bladerotation and blade translation based on the center image of the bladeand the center image of the slice; and motion-correcting the k-spacedata of the blade using the blade rotation and the blade translation;and updating the center image of the slice based on the motion-correctedk-space data of the blades in the slice; and jointly estimating slicerotation and slice translation based on the updated center images of theplurality of slices and the calibration data.
 9. The method of claim 1,wherein: jointly estimating rotation and translation further comprises:jointly estimating blade rotation and blade translation in each bladebased on the k-space data of the 3D imaging volume; jointly estimatingslice rotation and slice translation in each slice in the 3D imagingvolume based on the k-space data of the 3D imaging volume and thecalibration data; and computing final blade rotation and final bladetranslation based on the estimated blade rotation, the estimated bladetranslation, the estimated slice rotation, and the estimated slicetranslation; and correcting motion in the precorrection images furthercomprises correcting motion in the precorrection images using the finalblade rotation and the final blade translation.
 10. The method of claim1, wherein acquiring k-space data further comprises acquiring k-spacedata of the 3D imaging volume in a plurality of slice-encoding steps,for each slice-encoding step in the plurality of the slice-encodingsteps, the k-space data of the 3D imaging volume were acquired byrotating a blade in a kx-ky plane corresponding to the slice-encodingstep.
 11. The method of claim 1, wherein acquiring k-space data furthercomprises acquiring k-space data of the 3D imaging volume along aplurality of diffusion directions; and the method further comprises: foreach diffusion-weighting direction, jointly estimating rotation andtranslation based on k-space data of the 3D imaging volume of thediffusion-weighting direction and the calibration data; correcting themotion in precorrection images of the diffusion-weighting directionbased on the estimated rotation and the estimated translation; andoutputting the motion-corrected images of the diffusion-weightingdirection.
 12. The method of claim 11, wherein acquiring k-space datafurther comprises: acquiring the k-space data of the 3D imaging volume,wherein the k-space data of the 3D imaging volume were acquired byacquiring views in the blade in a center-out manner.
 13. The method ofclaim 11, wherein acquiring k-space data further comprises: acquiringthe k-space data of the 3D imaging volume, the k-space data of the 3Dimaging volume were acquired by acquiring views in the blade in asequential manner.
 14. The method of claim 1, wherein acquiring k-spacedata further comprises: acquiring the k-space data of the 3D imagingvolume, the 3D imaging volume is off from an iso-center of the MRsystem.
 15. The method of claim 1, wherein jointly estimating rotationand translation further comprises jointly estimating rotation andtranslation in the precorrection MR images based on images derived fromthe k-space data of the 3D imaging volume and images derived from thecalibration data.
 16. The system of claim 2, wherein the at least oneprocessor is further programmed to: jointly estimate blade rotation andblade translation in each blade based on the k-space data of the 3Dimaging volume; and iteratively fine-tune the blade translation.
 17. Thesystem of claim 2, wherein: the at least one processor is furtherprogrammed to acquire k-space data of a plurality of slices in the 3Dimaging volume, wherein for each slice in the plurality of the slices,the k-space data of the 3D imaging volume were acquired by rotating theblade in a kx-ky plane corresponding to the slice; and for each slice inthe 3D imaging volume, the at least one processor is further programmedto: combine k-space data in a center region of the blades of the sliceinto center k-space data of the slice; and reconstruct a center image ofthe slice based on the center k-space data of the slice; and the atleast one processor is further programmed to jointly estimate slicerotation and slice translation based on center images of the pluralityof slices and the calibration data.
 18. The system of claim 17, whereinthe at least one processor is further programmed to: for each slice inthe 3D imaging volume, for each blade in the slice, reconstruct a centerimage of the blade using center k-space data of the blade; jointlyestimate blade rotation and blade translation based on the center imageof the blade and the center image of the slice; and motion-correct thek-space data of the blade using the blade rotation and the bladetranslation; and update the center image of the slice based on themotion-corrected k-space data of the blades in the slice; and jointlyestimate slice rotation and slice translation based on the updatedcenter images of the plurality of slices and the calibration data. 19.The system of claim 2, wherein the at least one processor is furtherprogrammed to: jointly estimate blade rotation and blade translation ineach blade based on the k-space data of the 3D imaging volume; jointlyestimate slice rotation and slice translation in each slice in the 3Dimaging volume based on the k-space data of the 3D imaging volume andthe calibration data; compute final blade rotation and final bladetranslation based on the estimated blade rotation, the estimated bladetranslation, the estimated slice rotation, and the estimated slicetranslation; and correct motion in the precorrection images using thefinal blade rotation and the final blade translation.
 20. The system ofclaim 2, wherein the at least one processor is further programmed to:receive k-space data of the 3D imaging volume along a plurality ofdiffusion directions, wherein the k-space data of the 3D imaging volumewere acquired by acquiring views in the blade in a center-out manner;and for each diffusion-weighting direction, jointly estimate rotationand translation based on the k-space data of the 3D imaging volume ofthe diffusion-weighting direction and the calibration data; correct themotion in precorrection images of the diffusion-weighting directionbased on the estimated rotation and the estimated translation; andoutput the motion-corrected image of the diffusion-weighting direction.